Mr. Chip

process is*

Functorial in the pair (X,Y) I guess.

Hartshorne doesn't mention the process in functorial, but it seems like it should be.

Ah, yes, okay. This is one of the things I thought of. f: X to Z should yield a map between the completions, no?

By U I meant something other than you notated. I meant to refer to the tubular nhd.

I mean, we're looking at an infinitesimal thickening. I'm not sure I see how to pass from that to a true neighbourhood.

Would the right way to do it be to assume for contradiction no such U existed?

Hmm, okay, that makes a lot of intuitive sense. Thanks.

@DenisNardin, sorry

Denis: I'm afraid I don't know what you mean by a tubular nbd.

I guess my basic problem is a lack of intuition for what the global sections ("formal-regular functions") are or what they should tell us.

Say Y is a non-singular positive-dimensional subvariety of X = P_k^n, k alg. closed. It's possible to prove that k coincides with the global sections of the formal completion of X along Y. Can anyone suggest why that could help to prove the following: if f: X \to Z is a morphism sending Y to a point, where Z is a k-variety, then f sends X to a point. Thanks.

Nevermind, it's obvious when you look at it affine-locally.

I have a question which is so simple I don't really want to post it. Given a scheme X with global section s, suppose the stalk of s is zero in every residue field. Should s = 0? If so, why?

Is this an okay forum for me to ask about a question being put off hold? A friend of mine is new to the site and he's posted an entirely valid question, just not formatted right, and it was placed on hold. I've now helped him to fix it.

Okay, thanks anyway guys.

I can prove that A is dense, but I'm not sure how that helps.

I see.

Oh!

@PeterTamaroff: Sorry, what do you mean?

Similar such union within X, I mean.*

It feels like an application of the Baire category theorem, but I'm not sure how.

Well, I was hoping for a hint on a problem. Suppose X = A union B, where X is complete and B is a union of closed nowhere dense sets. I want to prove that A cannot be embedded in a similar such union.

Internet Relay Chat.

Hey guys. Is this place similar to #math on IRC?